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A346399
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a(n) is the number of symmetrically distributed consecutive primes centered at n (including n itself if n is prime).
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5
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0, 1, 1, 2, 3, 2, 1, 0, 4, 0, 1, 6, 1, 0, 6, 0, 1, 4, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 10, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 6, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 4, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 4, 0, 1, 0, 0, 2, 0
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OFFSET
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1,4
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COMMENTS
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a(n) is the number of consecutive primes in Goldbach pairs of 2n centered at n.
a(n) is odd if n is prime; otherwise, a(n) is even.
n is prime if a(n) = 1 and n is composite if a(n) = 0.
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LINKS
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EXAMPLE
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a(1) = 0 because no prime is <= 1.
a(2) = 1 because no prime is < 2 and {2} is the only symmetrically distributed prime centered at 2.
a(30) = 10 because there are 10 symmetrically distributed consecutive primes, {13, 17, 19, 23, 29, 31, 37, 41, 43, 47}, centered at 30.
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PROG
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(Python)
from sympy import isprime
for n in range(1, 100):
d = 1 if n%2 == 0 else 2
ct = 1 if isprime(n) else 0
while n - d > 2:
k = isprime(n+d) + isprime(n-d)
if k == 2: ct += 2
elif k == 1: break
d += 2
print(ct)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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